1
|
Chen M, Chen Y, Zhu Y, Jiang Y, Andelman D, Man X. Chain Flexibility Effects on the Self-Assembly of Diblock Copolymer in Thin Films. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Mingyang Chen
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Yuguo Chen
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Yanyan Zhu
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Ying Jiang
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - David Andelman
- School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
| | - Xingkun Man
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
- School of Physics, Beihang University, Beijing 100191, China
- Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
| |
Collapse
|
2
|
Chen G, Zhang H, Lu T, Jiang Y. The stress deformation response influenced by the chain rigidity for mesostructures in diblock copolymers. Phys Chem Chem Phys 2021; 23:22992-23004. [PMID: 34611676 DOI: 10.1039/d1cp03159g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A self-consistent field theory formalism based on the wormlike chain model is developed to investigate the stress-strain relation for mesostructures in diblock copolymers under the influence of chain rigidity, involving the adjustable simulation cell in the non-orthogonal coordinates by means of optimization of free energy. We elucidate the effect of the chain persistency broadly spanning from the Gaussian chain to the rigid rodlike chain on the elastic response of mesophases that deviate from the initial equilibrium structures. We analytically and numerically demonstrate that our current approach in the long chain limit recovers to the Gaussian-chain-based theory. Being ascribed to the distinct conformational behaviors for flexible chains and rigid rodlike chains, the tensile and compressive stresses applied to lamellae exhibit asymmetric deformation behaviors and the shear stress applied to the initial equilibrium hexagonal cylinders results in noticeable deviations in the shape and spatial arrangement of cylindroids for various chain rigidity values. For the zero stress, in addition, our approach can be straightforwardly utilized to explore the optimal size and shape of the simulation cell in order to achieve a stress free configuration of systems.
Collapse
Affiliation(s)
- Gaohang Chen
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Hui Zhang
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Teng Lu
- Computer Network Information Center of the Chinese Academy of Sciences, Beijing 100190, China
| | - Ying Jiang
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
| |
Collapse
|
3
|
Affiliation(s)
- Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| |
Collapse
|
4
|
Niu Y, Bu X, Zhang X. Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush. MATERIALS 2021; 14:ma14040778. [PMID: 33562209 PMCID: PMC7914892 DOI: 10.3390/ma14040778] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Revised: 01/28/2021] [Accepted: 02/04/2021] [Indexed: 11/21/2022]
Abstract
The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).
Collapse
|
5
|
Chen Y, Zhang X, Jiang Y. The influence of side-chain conformations on the phase behavior of bottlebrush block polymers. SOFT MATTER 2020; 16:8047-8056. [PMID: 32785406 DOI: 10.1039/d0sm00918k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A self-consistent field theory based on the wormlike chain model is implemented in the investigation of the self-assembly behavior of bottlebrush block polymers in the formation of a lamellar phase. We utilize the model in which the semi-flexible side chains of two types A and B are grafted at the semi-flexible backbone of type C to mimic the bottlebrush molecule, particularly allowing for the extended chain conformation due to the high grafting density. We examine the positional and orientational probability distribution for the segments along the backbone and side chains as a function of the grafting density and chain flexibility for all blocks, covering a broad regime spanning from the flexible chain to rigid rod chain. This reveals that the persistence length of side chains λSC which intrinsically tunes the chain conformation of bottlebrush polymers plays a pivotal role in determining the manner of the local monomer packing in microphase segregation. As an important adjustable factor, λSC has a remarkable impact on the backbone extension and then realizes the effective manipulation of the characteristic structural size of self-assembled microstructures, such as the domain spacing and the interfacial width.
Collapse
Affiliation(s)
- Yuguo Chen
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.
| | | | | |
Collapse
|
6
|
Lin TP, Chang AB, Luo SX, Chen HY, Lee B, Grubbs RH. Effects of Grafting Density on Block Polymer Self-Assembly: From Linear to Bottlebrush. ACS NANO 2017; 11:11632-11641. [PMID: 29072906 DOI: 10.1021/acsnano.7b06664] [Citation(s) in RCA: 69] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Grafting density is an important structural parameter that exerts significant influences over the physical properties of architecturally complex polymers. In this report, the physical consequences of varying the grafting density (z) were studied in the context of block polymer self-assembly. Well-defined block polymers spanning the linear, comb, and bottlebrush regimes (0 ≤ z ≤ 1) were prepared via grafting-through ring-opening-metathesis polymerization. ω-Norbornenyl poly(d,l-lactide) and polystyrene macromonomers were copolymerized with discrete comonomers in different feed ratios, enabling precise control over both the grafting density and molecular weight. Small-angle X-ray scattering experiments demonstrate that these graft block polymers self-assemble into long-range-ordered lamellar structures. For 17 series of block polymers with variable z, the scaling of the lamellar period with the total backbone degree of polymerization (d* ∼ Nbbα) was studied. The scaling exponent α monotonically decreases with decreasing z and exhibits an apparent transition at z ≈ 0.2, suggesting significant changes in the chain conformations. Comparison of two block polymer systems, one that is strongly segregated for all z (System I) and one that experiences weak segregation at low z (System II), indicates that the observed trends are primarily caused by the polymer architectures, not segregation effects. A model is proposed in which the characteristic ratio (C∞), a proxy for the backbone stiffness, scales with Nbb as a function of the grafting density: C∞ ∼ Nbbf(z). The scaling behavior disclosed herein provides valuable insights into conformational changes with grafting density, thus introducing opportunities for block polymer and material design.
Collapse
Affiliation(s)
- Tzu-Pin Lin
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
| | - Alice B Chang
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
| | - Shao-Xiong Luo
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
| | - Hsiang-Yun Chen
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
| | - Byeongdu Lee
- X-Ray Science Division, Advanced Photon Source, Argonne National Laboratory , Argonne, Illinois 60439, United States
| | - Robert H Grubbs
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
| |
Collapse
|
7
|
Mao S, MacPherson Q, Qin J, Spakowitz AJ. Field-theoretic simulations of random copolymers with structural rigidity. SOFT MATTER 2017; 13:2760-2772. [PMID: 28338151 DOI: 10.1039/c7sm00164a] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales comparable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density-density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density-density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies.
Collapse
Affiliation(s)
- Shifan Mao
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
| | | | | | | |
Collapse
|
8
|
Bu X, Zhang X. Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers. Polymers (Basel) 2016; 8:E301. [PMID: 30974614 PMCID: PMC6432401 DOI: 10.3390/polym8090301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 08/05/2016] [Accepted: 08/08/2016] [Indexed: 11/16/2022] Open
Abstract
The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory.
Collapse
Affiliation(s)
- Xiangyu Bu
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
| |
Collapse
|